Police say Brent was speeding when his car hit a curb and flipped.
Investigators believe alcohol was a contributing factor in the crash.
When officers came upon the scene, Brent was dragging 25-year-old Brown from the car.
Brown was pronounced dead at a nearby hospital.
Brown was an outside linebacker on the Dallas practice squad, having been released by the Indianapolis Colts in October.
Brent, 24, in his third season with the team, was booked into the Irving City Jail on one count of intoxication manslaughter — considered a second-degree felony that carries a potential two- to 20-year prison sentence with a maximum $10,000 fine.
Brent pleaded guilty to a DUI charge in 2009, according to court records in Champaign, Illinois.
The records list Brent, who played football with Brown at the University of Illinois, as Joshua Price-Brent, the same name listed in the Irving police report. The athlete got a 60-day sentence, a fine and 200 hours of community service.
Cowboys owner Jerry Jones said Saturday, “We are deeply saddened by the news of this accident and the passing of Jerry Brown.”
“At this time, our hearts and prayers and deepest sympathies are with the members of Jerry’s family and all of those who knew him and loved him,” he said in a statement.
The incident occurred shortly after 2 a.m. Saturday, one day before Dallas was scheduled to play the Bengals in Cincinnati.